What are the slope and the y-intercept of the linear function that is represented by the table?

Note: It seems you forgot to attach the table diagram. After a little research, I am able to find a table which is attached below.

Answer:

we conclude that:

Step-by-step explanation:

Finding the slope

Taking two points from the given table  (check the attached diagram)

Finding the slope between (-3/4, -1/30) and (-1/2, -2/15)

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{\frac{-2}{15}-\frac{-1}{30}}{\frac{-1}{2}-\frac{-3}{4}}[/tex]

[tex]m=-\frac{2}{5}[/tex]

Finding the y-intercept

We know that the slope-intercept form of the line equation is

[tex]y=mx+b[/tex]

where m is the slope and b is the y-intercept.

Given

substitute to find the y-intercept (b)

[tex]y=mx+b[/tex]

[tex]\left(\frac{-1}{30}\right)=-\frac{2}{5}\left(\frac{-3}{4}\right)+b[/tex]

switch sides

[tex]-\frac{2}{5}\left(\frac{-3}{4}\right)+b=\left(\frac{-1}{30}\right)[/tex]

[tex]\frac{3}{10}+b=\left(\frac{-1}{30}\right)[/tex]

[tex]\mathrm{Subtract\:}\frac{3}{10}\mathrm{\:from\:both\:sides}[/tex]

[tex]\frac{3}{10}+b-\frac{3}{10}=\frac{-1}{30}-\frac{3}{10}[/tex]

[tex]b=-\frac{1}{3}[/tex]

Therefore, we conclude that:

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